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Criteria for discrete spectrum of 1D Operators

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Communications in Mathematics and Statistics 2014年第3期2卷 279-309页

作者： Mu-Fa Chen School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems(Beijing Normal University)Ministry of EducationBeijing 100875People’s Republic of China

For discrete spectrum of 1D second-order differential/difference operators(with or without potential(killing),with the maximal/minimal domain),a pair of unified dual criteria are presented in terms of two explicit measures and the harmonic function of the ***,these criteria can be read out from the ones for the exponential convergence of four types of stability studied earlier,simply replacing the‘finite supremum’by‘vanishing at infinity’.Except a dual technique,the main tool used here is a transform in terms of the harmonic function,to which two new practical algorithms are introduced in the discrete context and two successive approximation schemes are reviewed in the continuous *** of them are illustrated by *** main body of the paper is devoted to the hard part of the story,the easier part but powerful one is delayed to the end of the paper.

关键词： discrete spectrum Essential spectrum Tridiagonal matrix(birth–death process) Second-order differential operator(diffusion) Killing

Structure of Essential Spectra and discrete spectrum of the Energy Operator of Six-Electron Systems in the Hubbard Model. First Quintet and First Singlet States

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Journal of Applied Mathematics and Physics 2022年第11期10卷 3424-3461页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of six-electron systems in the Hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the ... 详细信息

关键词： Hubbard Model Essential spectrum discrete spectrum Six Electron Systems Octet State Singlet State Quintet State

The Structure of Essential Spectra and discrete spectrum of Three-Electron Systems in the Impurity Hubbard Model—Quartet State

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Journal of Applied Mathematics and Physics 2021年第6期9卷 1391-1421页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a v-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.

关键词： Essential spectrum discrete spectrum Three-Electron System Local Impurity States Impurity Hubbard Model Quartet State Doublet State

Structure of Essential spectrum and discrete Spectra of the Energy Operator of Five-Electron Systems in the Hubbard Model. Third and Fourth Doublet States

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Journal of Applied Mathematics and Physics 2020年第12期8卷 2886-2918页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a v-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.

关键词： Essential spectrum discrete spectrum Five-Electron System Bound State Anti-Bound State Hubbard Model Doublet State Sextet State Quartet State

Contribution of vortex Rossby wave to spiral rainband formation in tropical cyclones

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Journal of Hydrodynamics 2014年第5期26卷 725-733页

作者：阮鲲查勇黄泓胡友彬 Key Laboratory of Virtual Geographic Environment of Ministry of Education College of Geographic ScienceNanjing Normal University College of Meteorology and Oceanography PLA University of Science and Technology School of Atmospheric Science Key Laboratory of Mesoscale Severe WeatherNanjing University

The contribution of the vortex Rossby wave （VRW） to framework of a barotropic non-divergent TC-like vortex model. the spiral rainband in the tropical cyclones （TCs） is studied in the The spectral function expanding method is used to analyze the disturbance evolution of a defined basic state vortex. The results show that the numerical solution of the model is a superposition of the continuous spectrum component （non-normal modes） and the discrete spectrum component （normal modes）. Only the eyewall and the rainbands in the inner core-region in a TC are related to the VRW normal modes, whereas the continuous spectrum wave components play an important role in the formation of secondary-, principal-, and distant- rainbands, especially the outer rainband, through an indirect way. The continuous spectrum can promote the development of the TC circulation for the occurrence of a mesoscale instability. The convection under a favorable moisture condition will trigger the inertial-gravitational wave to cause the formation of unstable spiral bandliked-disturbances outside of the eyewall. The complicated interaction between the basic state-vortex and the VRW disturbances will cause a positive feedback between the TC circulation and the rainband.

关键词： tropical cyclone spiral bands vortex Rossby wave continuous spectrum discrete spectrum

Hermitizable, isospectral complex second-order differential operators

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Frontiers of Mathematics in China 2020年第5期15卷 867-889页

作者： Mu-Fa CHEN Jin-Yu LI Research Institute of Mathematical Science Jiangsu Normal UniversityXuzhou 221116China School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Laboratory of Mathematics and Complex Systems(Beijing Normal University) Ministry of EducationBeijing 100875China

The first aim of the paper is to study the Hermitizability of secondorder differential operators,and then the corresponding isospectral *** explicit criteria for the Hermitizable or isospectral properties are *** second aim of the paper is to study a non-Hermitian model,which is now well *** a regular sense,the model does not belong to the class of Hermitizable operators studied in this paper,but we will use the theory developed in the past years,to present an alternative and illustrated proof of the discreteness of its *** harmonic function plays a critical role in the study of *** constructions of the function are *** required conclusion for the discrete spectrum is proved by some comparison technique.

关键词： Hermitizable isospectral differential operators non-Hermitianmodel discrete spectrum

On spectrum of Hermitizable tridiagonal matrices

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Frontiers of Mathematics in China 2020年第2期15卷 285-303页

作者： Mu-Fa CHEN Research Institute of Mathematical Science Jiangsu Normal UniversityXuzhou 221116China School of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex Systems(Beijing Normal University)Ministry of EducationBeijing 100875China

This paper is devoted to the study on the spectrum of Hermitizable tridiagonal *** an illustration of the application of the author’s recent results on Hermitizable matrices,an explicit criterion for discrete spectrum of the matrices is presented,with a slight and technical *** problem is well known,but from the author’s knowledge,it has been largely opened for quite a long *** is important in various application,in quantum mechanics for *** main tool to solve the problem is the isospectral technique developed a few years *** alternative constructions of the isospectral operator are presented;they are helpful in theoretical analysis and in numerical computations,*** illustrated examples are included.

关键词： Hermitizable birth-death matrix isospectral matrices discrete spectrum

Intersections of Homogeneous Cantor Sets with Their Translations

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Acta Mathematica Sinica,English Series 2008年第8期24卷 1313-1318页

作者： Mei Feng DAI Nonlinear Scientific Research Center Faculty of Science Jiangsu University Zhenjiang 212013 P. R. China

We pursue the study on homogeneous Cantor sets with their translations. We get the fractal structure of intersection I（t）, and find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from shifting numbers with the coding of t. Concretely, a very brief calculation formula of the measure with the coding of t is given.

关键词： homogeneous Cantor set intersection fractal structure discrete spectrum

Regionally proximal relation of order d along arithmetic progressions and nilsystems

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Science China Mathematics 2020年第9期63卷 1757-1776页

作者： Eli Glasner Wen Huang Song Shao Xiangdong Ye School of Mathematics Tel Aviv UniversityTel Aviv 6997801Israel CAS Wu Wen-Tsun Key Laboratory of Mathematics and School of Mathematics University of Science and Technology of ChinaHefei 230026China

The regionally proximal relation of order d along arithmetic progressions,namely AP[d]for d 2 N,is introduced and *** turns out that if(X;T)is a topological dynamical system with AP[d]=Δ,then each ergodic measure of(X;T)is isomorphic to a d-step pro-nilsystem,and thus(X;T)has zero ***,it is shown that if(X;T)is a strictly ergodic distal system with the property that the maximal topological and measurable d-step pro-nilsystems are isomorphic,then AP[d]=RP[d]for each d 2 *** follows that for a minimal 1-pro-nilsystem,AP[d]=RP[d]for each d 2 *** example which is a strictly ergodic distal system with discrete spectrum whose maximal equicontinuous factor is not isomorphic to the Kronecker factor is constructed.

关键词： regionally proximal relation pro-nilsystem discrete spectrum equicontinuous factor